Prototype

There is one prototype of pbsvx available, please see below.

pbsvx( const char fact, MatrixAB& ab, MatrixAFB& afb, char& equed,
        VectorS& s, MatrixB& b, MatrixX& x, Scalar >, VectorFERR& ferr,
        VectorBERR& berr );

Description

pbsvx (short for $FRIENDLY_NAME) provides a C++ interface to LAPACK routines SPBSVX, DPBSVX, CPBSVX, and ZPBSVX. pbsvx uses the Cholesky factorization A = U**H*U or A = LL*H to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite band matrix and X and B are N-by-NRHS matrices.

Error bounds on the solution and a condition estimate are also provided.

Description =====

The following steps are performed:

1. If FACT = 'E', real scaling factors are computed to equilibrate the system: diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B Whether or not the system will be equilibrated depends on the scaling of the matrix A, but if equilibration is used, A is overwritten by diag(S)*A*diag(S) and B by diag(S)*B.

2. If FACT = 'N' or 'E', the Cholesky decomposition is used to factor the matrix A (after equilibration if FACT = 'E') as A = U*H * U, if UPLO = 'U', or A = L * L*H, if UPLO = 'L', where U is an upper triangular band matrix, and L is a lower triangular band matrix.

3. If the leading i-by-i principal minor is not positive definite, then the routine returns with INFO = i. Otherwise, the factored form of A is used to estimate the condition number of the matrix A. If the reciprocal of the condition number is less than machine precision, INFO = N+1 is returned as a warning, but the routine still goes on to solve for X and compute error bounds as described below.

4. The system of equations is solved for X using the factored form of A.

5. Iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it.

6. If equilibration was used, the matrix X is premultiplied by diag(S) so that it solves the original system before equilibration.

The selection of the LAPACK routine is done during compile-time, and is determined by the type of values contained in type MatrixAB. The type of values is obtained through the value_type meta-function typename value_type<MatrixAB>::type. The dispatching table below illustrates to which specific routine the code path will be generated.

Definition

Defined in header boost/numeric/bindings/lapack/driver/pbsvx.hpp.

Parameters or Requirements on Types

Complexity

Example

#include <boost/numeric/bindings/lapack/driver/pbsvx.hpp>
using namespace boost::numeric::bindings;

lapack::pbsvx( x, y, z );

this will output

[5] 0 1 2 3 4 5

Notes

See Also